Interactivate

Misleading Graphs

Abstract

This lesson will challenge students to think creatively by having them design and build water
balloon catchers from random scrap materials, while requiring them to take into consideration a
multitude of variables including: cost, maintenance, total capacity, etc. After completing their
water balloon catchers, students will collect data based on the performance of all catchers
designed by the class. Students will then construct at least two bar graphs to be used in a
commercial advocating the purchase of their group's catcher.

Summarize, represent, and interpret data on a single count or measurement variable

Third Grade

Measurement and Data

Represent and interpret data.

Grades 3-5

Algebra

Use mathematical models to represent and understand quantitative relationships

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

Select and use appropriate statistical methods to analyze data

Grade 5

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Grade 7

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Grade 8

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Introductory Mathematics

Algebra

COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Data Analysis and Probability

COMPETENCY GOAL 3: The learner will understand and use graphs and data analysis.

5th grade

Data Analysis and Probability

The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.

The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of b

7th Grade

Data Analysis and Probability

The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples.

5th Grade

Probability and Statistics

5.19 The student will find the mean, median, mode, and range of a set of data.

Student Prerequisites

Technological: Students must be able to:

perform basic mouse manipulations such as point, click and drag

use a browser for experimenting with the activities

Teacher Preparation

access to a browser

access to a variety of scrap materials to design and construct water ballooon catchers

rulers and scissors

Key Terms

bar graph

A diagram showing a system of connections or interrelations between two or more things by using bars

boxplot

histogram

A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval

line graph

A diagram showing a system of connections or interrelations between two or more things by using lines

mean

The sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean

median

"Middle value" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50%

mode

For lists, the mode is the most common (frequent) value. A list can have more than one mode. For histograms, a mode is a relative maximum ("bump"). A data set has no mode when all the numbers appear in the data with the same frequency. A data set has multiple modes when two or more values appear with the same frequency.

pie graph

A diagram showing a system of connections or interrelations between two or more things by using a circle divided into segments that look like pieces of pie

probability

The measure of how likely it is for an event to occur. The probability of an event is always a number between zero and 100%. The meaning (interpretation) of probability is the subject of theories of probability. However, any rule for assigning probabilities to events has to satisfy the axioms of probability

Lesson Outline

Focus and Review

Review vocabulary covered to this point

Review all types of graphs you have covered to this point

Explain the term misleading graph

Begin a discussion on how misleading graphs are used in advertising

Objectives

Let the students know what they will be doing and learning today. Say something like this:

Today, class, we are going to learn about how graphs can sometimes be misleading.

We are going to use the computers to make our own graphs and learn how to analyze and compare
those graphs, but please do not turn your computers on until I ask you to. I want to show you
a little about these activities first.

Allow time for the students to familiarize themselves with the applets while you circulate
throughout the room answering any questions.

Independent Practice

Have students turn off their monitor.

Explain to the students their assignment and following the explanation have students
construct their catchers:

You are to work in pairs to construct a water balloon catcher. You have been alloted X
amount of dollars to purchase supplies. (Have a store set up in the rear of the room.
Materials can consist of almost any type of scrap you can collect from around the school,
your home, or that your students collect and donate.) After these water balloon catchers are
complete we will test them as a class. Each group will have the opportunity to drop 10 water
balloons into their catcher in order to collect data on their group's catcher and their
competitor's catchers based on:

How many water balloons landed in the catcher?

How many water balloons completely missed the catcher?

How many water balloons dropped into the catcher and bounced out?

Total number of balloons the catcher will hold at any given time.

Did the catcher require any maintenance?

Number of broken balloons.

Number of balloons caught without breaking.

Cost of balloon catcher.

Total cost of balloon catcher including maintenance fees.

Once all the data has been collected you will design a commercial enticing people to
purchase your water balloon catcher over your competitor's. You will need to include at
least two graphs in your commercial. (These graphs can be misleading but are not required to
be.)

After students construct their water balloon catchers, they should collect data on the
data sheet as a class.